Sanders J.A., Verhulst F. — Averaging methods in nonlinear dynamical systems :: Электронная библиотека попечительского совета мехмата МГУ

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Sanders J.A., Verhulst F. — Averaging methods in nonlinear dynamical systems

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Название: Averaging methods in nonlinear dynamical systems

Авторы: Sanders J.A., Verhulst F.

Аннотация:

In this book we have developed the asymptotic analysis of nonlinear dynamical systems. We have collected a large number of results, scattered throughout the literature and presented them in a way to illustrate both the underlying common theme, as well as the diversity of problems and solutions. While most of the results are known in the literature, we added new material which we hope will also be of interest to the specialists in this field.

Язык:

Рубрика: Физика/Динамические системы/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1985

Количество страниц: 247

Добавлена в каталог: 28.09.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Gravitational force      224
Gravitational perturbation      224
Gravitational potential      217 219
Gronwall      3 6 17 23 38 39 45 47 54 79 92 110 116 117 187 193
Hamilton equation      132 136 184 233 234
Hamilton — Jacobi      184
Hamiltonian      132—134 136 137 141 143—147 150 152—154 163 164 167 168 170 174 223 233 235
Hamiltonian analytic      143
Hamiltonian extended      152
Hamiltonian flow      132
Hamiltonian formulation      232
Hamiltonian framework      185
Hamiltonian function      184
Hamiltonian linearized      143
Hamiltonian mechanics      143 185 233
Hamiltonian normalized      153 162 163 165 167 169
Hamiltonian perturbation      27 190
Hamiltonian structure      184
Hamiltonian system v      27 34 66 102 125 132 143—145 167 223 224
Hamiltonian vectorfield      136
hessian      234
Heteroclinic      201
Hilbert D.      9
Homoclinic      201
Hyperbolic      120 155 165 229
Hyperbolic critical point      162
Hyperbolic density law      226
Hyperbolic normal mode      153 173 174
Hyperbolic orbit      155 159 162 228
Hyperbolic periodic orbit      160
Hyperbolic periodic solution      120
Hyperbolic solution      153 229
Implicit function theorem      91 202
Inclination      183 221 224
Inclination critical      223 224
INDEX      153 235
Inner boundary layer      161
Inner domain      104 105 112 118
Inner equation      103 104 110 118 122
Inner expansion      102—105 109
Inner product      132
Inner region      102—105 114 117
Inner variable      104
Inner vectorfield      102
Inner-outer expansion      104 105
Inner-outer vectorfield      104 105
Integrability      169—171 174 217
Integrable      118 154 163 168 171 172 174 217 220 222 224
Integrable formally      174
integral      9 10 43 57 108 115 150 153 154 163—166 171—175 191 217 220 221
Integral approximate      108 162 165
Integral definite      226
Integral elliptic      119 120 126
Integral energy      119 221
Integral equation      6 16 182
Integral formal      174
Integral Fresnel      109
Integral manifold      34 108
Integral of motion      217 220 229 234 235
Integral third      163 166—172 174 175 220
integrand      90 98
Integrate      56 89 182 186 191 195 202 220
Integration      4 26 27 56 61 94 182 191
Integration constant      90 98
Integration numerical      28 32 76 82
Integration partial      14 108
Interact      121
Interaction degrees of freedom      163
Interaction modes      173
Interaction number      164
Interaction planets      181
Interaction self      142
Interaction species      19 67—69 74
Intersection (of stable and unstable manifold)      202
Invariant      76 77 133 166 167 234 235
Invariant adiabatic      94 101
Invariant circle      149
Invariant flow      102 144 147
Invariant manifold      34 143 147—149 201
Invariant point      153
Invariant subspace      144
Invariant subsystem      171
Invariant surface      165
Invariant torus      143 144 149 162
Jacobi C.G.J.      184—186
Jacobi C.G.J. Hamilton      184
Jacobian determinant      196
Jacobian elliptic functions      195 196
Jordan normal form      124
Josephson equation      203
Kam theorem      144
KBM - vectorfield      36 39—41 43—46 48 55 70 71 75
Kepler motion      185 216
Kepler problem      216—219
Kolmogorov A.N.      144
Lagrange J.—L.      33 67 68 71 73 74 77 213
Lagrange J.—L. multipliers      152
Landau symbol      11
Layer      229
Layer boundary      102—104 161
Legendre polynomial      219
Lie-transform      132
Limit-cycle      25 73 78
Limit-cycle attracting      78 213
Limit-cycle stable      25
Linear      61 79 94 122 127 144 147 162 209 232
Linear algebra      124
Linear approximation      71 73 82
Linear attraction      82
Linear behavior      5
Linear damping      30 61 68 81 82
Linear equation      5 75 192 209
Linear independence      19 165
Linear operator      124
linear oscillator      25 42 48 84
Linear system      26 79 206 212
Linear transformation      26 124 166 169
Linearity      124
Linearization      80
Linearize      5 143 144 146 147 155 161 206
Lipschitz condition      2 3
Lipschitz constant      2 18 36 40 45 54 92 96 99
Lipschitz continuity      17 22 36 38 39 45 46 193
Lipschitz continuous      16 21 35 36 38 39 43 50 53 55 64 74
local      102 106 123 143 231 232
Local analysis      143
Local average      34 35
Local character      102 146
Local coordinates      126 128 132 134 136 137 231 233 234
Local diffeomorphism      234 235
Local expansion      103
Local transversal      146
Local variable      102
LOCK      107 118
Locking      118
Locking resonance      106 107 118 122 123
Lyapunov A.M.      5 143
Lyapunov A.M. function      42
Lyapunov A.M. stability      4 5 214
Manifold      102 126 149 161 231—233
Manifold compact      146
Manifold energy      144 146 147
Manifold integral      34 108
Manifold invariant      34 143 147—149 201
Manifold resonance      102—104 106 107 112 114 117 121 123 161
Manifold stable      103 118 202 208
Manifold symplectic      233
Manifold two-dimensional      143
Manifold unstable      118 202
Mass      60 226

Mass decrease      229
Mass distribution      219
Mass exchange      216
Mass increase      229
Mass loss      59 100 226
Mass point      217 219
Mass slowly varying      33
Mass total      100 218 229
Mass variable      100
Matching      104 109
Mathieu equation      25 26
Mechanical system      59
Mechanics      42 97 183 184 232
Mechanics celestial      Celestial mechanics
Mechanics classical      11
Mechanics Hamiltonian      143 185 233
Mechanics satellite      219
Melnikov function      120 199 201—203
Melnikov map      146 148
Melnikov section      153 159
Mitropolsky, Ya.A. v      23 34 36 52 60 83 187
MODE      173
Mode normal      144 146—155 158—160 165 166 169—174
Model      74 121 224
Model population growth      19
Model problem      207 208
Moment of inertia      86
Momentum      132 229 234
Momentum angular      101 217 218 220 221 225 226
Momentum mapping      154
Morse function      234
Morse theory      151 234 235
Moser J.      144 216
Multiple time scale      34 118 189 190 207
Multiplier, Lagrange      152
Near-identuity transform      125 128 134 210
Nearly-circular      101
Newton I.      181
Newtonian      100 217
Non-existence of integral      174
Nonlinear      16 70 125 161 187 212
Nonlinear damping      81
Nonlinear differential equation      15 124
Nonlinear equation      85 212
Nonlinear force      86 226
Nonlinear friction      224
Nonlinear oscillation v      9 20 186 187
Nonlinear oscillator      85 171
Nonlinear perturbation      61 210
Nonperiodic      93 183
Normal bundle      152
Normal form v      124—133 136 138 141 143 145 149—151 154 158 159 165—173 204
Normal mode      144 146—155 158—160 165 166 169—174
Normal system      172
Normalization      129 132 136 162 173 174
Normalize      141 153 154 162 163 165—171 173 174
Normalizing      133 138 141 163 165 171
Oblate planet      219—221 224 225
Orbit      25 73 81 108 109 144 146 149 153 155 159 161 171 172 182 208 216 218 223 224 229
Orbit bound      228
Orbit critical      152
Orbit elliptic      101 153 155 162 163 228
Orbit equatorial      223 224
Orbit escape      228
Orbit flip      153
Orbit general position      169
Orbit hyperbolic      155 159 162 228
Orbit measure      144
Orbit parabolic      228
Orbit periodic      143 145 146 149 150 152—154 156 159 160 163 164 166 167 172—174 204—206 218
Orbit perturbation      71
Orbit phase      25 31
Orbit planar polar      223
Orbit regular      144
Orbit satellite      220
Orbit stable      172 174
Orbital element      101 228
Orbital plane      221
Order function      11—16 23 34 72 76 102
Order of magnitude      12 41 42 82 213
Oscillate      30
Oscillation nonlinear v      9 20 186 187
Oscillation triode      186
Oscillator      30 42 43 61 81 83 86 121
Oscillator anharmonic      68
Oscillator harmonic      27 60 69 216 218 220 224
Oscillator linear      25 2 48 84
Oscillator nonlinear      85 171
Outer      104
Outer domain      114 115 161 162
Outer equation      114
Outer expansion      103 104 109
Outer inner      Inner-outer
Outer region      103 104 114 115
Parabolic nearly-      101 228 229
Parabolic orbit      228
Passage      59 60
Passage peri-astron      218
Passage through resonance      Resonance
Pendulum      59 60
Pendulum Einstein, A.      84 89 93
Pendulum mathematical      18 61 119 195
Pendulum perturbed      119
Period      27 39 51 106 167 218
Period (in real time)      187
Periodic      21 24 26 29 34—36 39 43 50—52 62—64 72 83 87 97 106 120 125 128 147 151 167 169 185 190 192 218 222 223 225 227
Periodic averaging      34 39
Periodic differential equation      187
Periodic function      55 183
Periodic motion      150
Periodic orbit      143 145 146 149 150 152—154 156 159 160 163 164 166 167 172—174 204—206 218
Periodic solution vi      25 27 34 51 52 66 80 118 143 144 146 147 149 150 153 160—163 165 166 169—174 185 186
Periodic system      34
Periodic vectorfield      56
Periodically      119
periodicity      35 187 228
Perturb      79 183 218
Perturbation      1 21 60 66 79 106 169 181—183 185 196 218 221 224
Perturbation autonomous      69
Perturbation Duffing-type      61
Perturbation equation      20 21 24 26 65 74 85 93 101 183—185
Perturbation force      224
Perturbation formulation      183 186 221
Perturbation gravitational      224
Perturbation Hamiltonian      27 224
Perturbation method      181 183 186
Perturbation nonlinear      61
Perturbation of orbits      71
Perturbation oscillator      216
Perturbation planetary      186 187
Perturbation problem      10 15 18—21 25 33 36 50 119 190 222 225
Perturbation procedure      182
Perturbation regular      213
Perturbation scheme      89 111
Perturbation secular      33 183 186
Perturbation singular      190
Perturbation technique      74 186 224
Perturbation theory      3 134 181 185—187 190 210 218
Perturbation vector      220
Perturbed elliptic orbit      101
Perturbed equation      212
Perturbed initial valua problem      20
Perturbed motion      181 185 216
Perturbed operator equation      76
Perturbed pendulum      18 119
Perturbed planet      183
Perturbed problem      16 184 218 219
Perturbed system      201
Planet      181 183 187
Planet Earth      219

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